Coinage metal diatomic molecules are building blocks for nanostructured materials, electronic devices, and catalytically or photochemically active systems that are currently receiving lively interest in both fundamental and applied research. The theoretical study presented here elucidates the electronic structure in the ground and several low-lying excited states of the diatomic molecule CuAu that result from the combination of the atoms in their ground states nd(10)(n + 1)s(1) S-2 and lowest excited d-hole states nd(9)(n + 1)s(2) D-2 (n = 3 for Cu, n = 5 for Au). Full and smooth potential energy curves, obtained at the multireference configuration interaction (MRCI) level of theory, are presented for the complete set of the thus resulting 44 Lambda-S terms and 86 Omega terms. Our approach is based on a scalar relativistic description using the Douglas-Kroll-Hess (DKH) Hamiltonian, with subsequent perturbative inclusion of spin-orbit (SO) coupling via the spin-orbit terms of the Breit-Pauli (BP) Hamiltonian. The Omega terms span an energy interval of about 7 eV at the ground state's equilibrium distance. Spectroscopic constants, calculated for all terms, are shown to accurately reproduce the observation for those nine terms that are experimentally known.